It's not really fascism, but it's not just authoritarianism either. There are many different kinds of authoritarianism.
"Fascism" was applied to several different situations where a legal government became more and more dictatorial. It also connotes nationalism, originally applied to right-wing groups rather than left-wing groups.
It has since been applied so widely as generically "intolerant and authoritarian", but this article is using it in a sense slightly closer to the way it was applied by Mussolini and then Franco. In particular, it's focusing on the ethnic nationalism aspect of it, and there the article is focusing on specific factors of US national life.
If one wanted to be super originalistic in the way the term is used, it would apply only to the Mussolini regime, because that's where the word was coined. By that definition the Nazis aren't fascists, either.
Anybody using the term will have to be clear how loosely they're applying it. In this case, the author is drawing real historical parallels to both the Mussolini regime and other related nationalist, totalitarian regimes. It's not historically illiterate.